Bracewell joined Sunderland's academy coaching staff in 2013 and was promoted to the first team under Dick Advocaat in 2015, where he remainder under successors Sam Allardyce and Moyes.
A statement on the club's official website on Saturday confirmed that he will step down, however, as the search for a new head coach goes on.
"It has been a great honour to serve Sunderland AFC as a player, coach and assistant manager for a combined total of 10 years," Bracewell said.
"I would like to thank the club and its staff, but also the supporters for the great backing I have received throughout my Sunderland career. I now look forward to the next challenge in my football career."